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MathGroup Archive 2005

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Correct errors on fit parameter ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55406] Correct errors on fit parameter ?
  • From: Bruyndonckx P <pbruynd at vub.ac.be>
  • Date: Tue, 22 Mar 2005 03:50:56 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Is there an easy way to obtain the correct statistical error on fitted parameters ?

I tried the following simple example :

x=Range[5];
y=x^2;
yerror={10,10,10,10,10}

NonlinearRegress[Transpose[{x, y}], a + b*xx + c*xx^2, {xx}, {a, b, c}, Weights -> 1/yerror^2, RegressionReport -> {ParameterCITable}]


The asymptotic error and confidence intervals are of the order of 10^-15 !!!!.   Obviously the weights (errors or uncertainty on the data) are not taken 
into account when computing the error on the parameter.  It seems that the SE is only based on the residuals, which are nearly 0 is this case because the 
fit is 
perfect.  Changing the value of the errors has no impact on the standard errors of the fit parameters.

Using the Regress command makes no difference.

Through other examples I have found that the errors are taking into account correctly to find the correct value of the fit parameters but NOT to compute 
the statistical error on the fit parameter.

I presume other experimental scientist must have faced this problem when analyzing data.

Any suggestions ?

Thanks,

Peter


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